Method and system using ternary sequences for simultaneous transmission to coherent and non-coherent receivers

ABSTRACT

The present invention describes a method and system for simultaneous transmission of data to coherent and non-coherent receivers. The method at the transmitter includes retrieving a base ternary sequence having a pre-defined length, obtaining one or more ternary sequences corresponding to data to be transmitted and transmitting the obtained one or more ternary sequences by the transmitter. The method steps at the receiver includes receiving one or more ternary sequences corresponding to the data transmitted, demodulating each of the received ternary sequences by correlating with all cyclic shifts of the base ternary sequence by the receiver if the receiver is a coherent receiver, demodulating each of the received ternary sequences by correlating with all cyclic shifts of the absolute of the base ternary sequence by the receiver if the receiver is a non-coherent receiver and detecting the transmitted data based on the cyclic shifts corresponding to maximum correlation values.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a Continuation Application of a U.S. applicationSer. No. 15/028,645, filed on Apr. 11, 2016, which is National StageApplication of International Application No. PCT/KR2014/009873, filed onOct. 21, 2014, which claims the benefit under 35 USC 119(a) of IndianPatent Application No. 4875/CHE/2013 filed Sep. 26, 2014, in the IndianIntellectual Property Office.

TECHNICAL FIELD

The present invention relates to communication system and moreparticularly relates to method and system for coherent and non-coherentdata transmission.

BACKGROUND ART

Low power wireless networks such as sensor networks, PAN (personalaccess network), BAN (body area network), etc., have received anincreasing interest for industrial automation, personalizedentertainment and personal healthcare. Typically the devices in thesenetworks are small in size and are required to conserve their batterylife. Therefore, it is needed that they operate at low power though witha relatively low symbol rates. The choice of efficient transmission andreception protocols which trade-off energy with symbol rate become animportant aspect in the design of low power wireless networks.

The form of signal processing algorithms employed at the receiver isvery critical to the design of energy-efficient transmission protocols.It is well-known that receivers are broadly classified into coherent andnon-coherent receivers. A coherent receiver makes use of the phaseinformation in demodulation of symbols, whereas a non-coherent receiveris mainly based on envelope detection with no phase information.Typically, coherent receivers yield better performance than thenon-coherent receivers at the cost of power and complexity. Due to thecapability of exploiting the phase information, coherent communicationsupports bi-polar modulation alphabets whereas non-coherentcommunication supports unipolar alphabets. Thus, typically, acommunication network is designed so as to exclusively support eithercoherent or non-coherent receivers. However, many communication networkswhich involve low power constraints might be required to support bothcoherent and non-coherent receptions. This stems from the fact that somereceivers employ non-coherent reception due to the system processing andpower constraints. Therefore, in such networks, transmission schemeneeds to be designed to ensure that it is suitable for both types ofreceivers. Further, in many cases, due to practicability, transmitter isassumed to be agnostic of the type of the target receiver, therebymaking the design task more challenging.

DISCLOSURE OF INVENTION Solution to Problem

An objective of present invention is to transmit data in low powerdevices.

Yet another objective of the present invention is to transmit data tocoherent and non-coherent receivers simultaneously.

An embodiment of present invention describes a method of transmittingdata. The method comprises retrieving a base ternary sequence having apre-defined length, obtaining one or more ternary sequencescorresponding to data to be transmitted from the base ternary sequenceand transmitting the obtained ternary sequences by the transmitter.According to one embodiment of present invention, obtaining one or moreternary sequences corresponding to data to be transmitted from the baseternary sequence comprises dividing the data to be transmitted into oneor more symbols having a pre-defined length and mapping one or moresymbols in binary form to the one or more ternary sequences obtained asone or more cyclic shifts of the base ternary sequence, wherein thenumber of said cyclic shifts is determined based on one to one mappingfrom symbols to ternary sequences obtained as the said cyclic shifts.

One aspect of present invention discloses the generation of base ternarysequence having a pre-defined length. The method of generating the baseternary sequence comprises selecting a seed sequence of pre-definedlength, wherein the seed sequence is one of an m-sequence and complementof an m-sequence, generating a perfect ternary sequence from the seedsequence if the weight of the seed sequence is a perfect square, whereinthe weight of a sequence is the number of non-zero elements in asequence, generating a near perfect ternary sequence from the seedsequence if the weight of the seed sequence is different from a perfectsquare and inserting a pre-defined binary value in a pre-definedlocation of the perfect ternary sequence or the near perfect ternarysequence for generating the base ternary sequence.

Another aspect of present invention discloses a method of receiving datatransmitted from one or more transmitter. According to one embodiment ofpresent invention, the method comprises receiving by a receiver one ormore data-symbols transmitted as one or more ternary sequences from theone or more transmitter, demodulating the ternary sequence bycorrelating the received signal with all the cyclic shifts of the baseternary sequence in case the receiver is a coherent receiver,demodulating by correlating the received signal with all the cyclicshifts of the absolute of the base ternary sequence in case the receiveris a non-coherent receiver, detecting each of the transmitteddata-symbols based on the cyclic shift corresponding to the maximumcorrelation. In this respect, a cyclic shift of the base ternarysequence is a ternary sequence obtained by cyclically shifting the baseternary sequence to the left or right. For instance, if x is a baseternary sequence of length N, whose elements are given by x₀, x₁, . . .x_(N). Then a cyclic shift of two, of the base ternary sequence iseither x₂ . . . x_(N), x₀, x₁ or x_(N-1), x_(N), . . . , x₀x₁. There areN distinct cyclic shifts of the base ternary sequence and the saidcyclic shifts of the base ternary sequence can be obtained by cyclicallyshifting in either direction, so long as the direction of every cyclicshift remain the same.

Another aspect of present invention discloses a transmitter. Thetransmitter comprises a data input module, a transmitting module, asymbol generating module coupled with the data input module adapted forgenerating one or more data-symbols based on input data, a ternarysequence generating module coupled with the symbol generating module, abase ternary sequence retrieving module and a cyclic shift generatingmodule. The base ternary sequence retrieving module retrieves the baseternary sequence. Likewise, the cyclic shift generating module isadapted for generating cyclic shifts of base ternary sequence based onthe generated data-symbols

Further, the present invention discloses a base ternary sequencegenerating module. The base ternary sequence generating module comprisesa seed sequence selection module, a perfect ternary sequence generationmodule, a near perfect ternary sequence generation module and apre-defined value insertion module. The seed sequence selection moduleis adapted for selecting the seed sequence as an m-sequence orcomplement of an m-sequence. If N is the length of the base ternarysequence, the weight of the seed sequence is N/2, if the selected seedsequence is an m-sequence. Likewise, the weight of the seed sequence isequal to (N−2)/2, if the selected seed sequence is complement of anm-sequence.

Furthermore, the present invention discloses a receiver. The receiveraccording to one embodiment of present invention comprises a signalreceiving module, a demodulating module coupled with a ternary sequenceinput module and the signal receiving module and a symbol detectionmodule. The ternary sequence input module retrieves all the N cyclicshifts of the base ternary sequence, if the receiver is a coherentreceiver. The ternary sequence input module retrieves all N cyclicshifts of the absolute of the base ternary sequence, if the receiver isa non-coherent receiver. In this regard, N is the length of the baseternary sequence and would be referred at many places in the document.The signal receiving module is adapted for receiving a signaltransmitted from a transmitter.

The demodulating module demodulates the received signal by correlatingthe received signal with the sequences from ternary sequence inputmodule.

The symbol detection module is adapted for detecting each of thetransmitted data-symbols by identifying the cyclic shift of the baseternary sequence that corresponds to maximum correlation value among allthe N correlation values corresponding to N sequences from ternarysequence input module, obtained by the demodulating module andsubsequently mapping the identified cyclic shift to the data-symbolsusing the inverse of one to one mapping that was employed at thetransmitter

BRIEF DESCRIPTION OF DRAWINGS

The aforementioned aspects and other features of the present inventionwill be explained in the following description, taken in conjunctionwith the accompanying drawings, wherein:

FIG. 1 is a block diagram of an exemplary communication system,according to one embodiment of present invention.

FIG. 2 is a block diagram depicting data processing operation in anexemplary communication system, according to one embodiment of presentinvention.

FIG. 3 is a flow diagram illustrating a method of transmitting data,according to one embodiment of present invention.

FIG. 4 is a flow chart illustrating a method of obtaining one or moreternary sequences corresponding to data to be transmitted

FIG. 5 is a flow chart illustrating a method of generating a baseternary sequence, according to one embodiment of present invention.

FIG. 6 is a flow diagram illustrating a method of generating a perfectternary sequence from the seed sequence, according to one embodiment ofpresent invention.

FIG. 7 is a flow diagram illustrating a method of generating a nearperfect ternary sequence, according to one embodiment of presentinvention.

FIG. 8 is block diagram of a transmitter, according to one embodiment ofpresent invention.

FIG. 9 is block diagram of a base ternary sequence generating module,according to one embodiment of present invention.

FIG. 10 is block diagram of a receiver, according to one embodiment ofpresent invention.

FIG. 11 is a block diagram of an exemplary communication device showingvarious components for implementing embodiments of the presentinvention.

MODE FOR THE INVENTION

The embodiments of the present invention will now be described in detailwith reference to the accompanying drawings. However, the presentinvention is not limited to the embodiments. The present invention canbe modified in various forms. Thus, the embodiments of the presentinvention are only provided to explain more clearly the presentinvention to the ordinarily skilled in the art of the present invention.In the accompanying drawings, like reference numerals are used toindicate like components.

The specification may refer to “an”, “one” or “some” embodiment(s) inseveral locations. This does not necessarily imply that each suchreference is to the same embodiment(s), or that the feature only appliesto a single embodiment. Single features of different embodiments mayalso be combined to provide other embodiments.

As used herein, the singular forms “a”, “an” and “the” are intended toinclude the plural forms as well, unless expressly stated otherwise. Itwill be further understood that the terms “includes”, “comprises”,“including” and/or “comprising” when used in this specification, specifythe presence of stated features, integers, steps, operations, elementsand/or components, but do not preclude the presence or addition of oneor more other features integers, steps, operations, elements,components, and/or groups thereof. As used herein, the term “and/or”includes any and all combinations and arrangements of one or more of theassociated listed items.

Unless otherwise defined, all terms (including technical and scientificterms) used herein have the same meaning as commonly understood by oneof ordinary skill in the art to which this disclosure pertains. It willbe further understood that terms, such as those defined in commonly useddictionaries, should be interpreted as having a meaning that isconsistent with their meaning in the context of the relevant art andwill not be interpreted in an idealized or overly formal sense unlessexpressly so defined herein.

FIG. 1 is a block diagram of an exemplary communication system,according to one embodiment of present invention. According to oneembodiment of present invention, the communication system comprises atransmitter 101 and one or more receivers. The receiver according to oneembodiment of present invention is one of coherent receiver such as102A, 102B . . . 102N and non-coherent receiver such as 103A, 103B . . .103N. The transmitter 101 and receivers are connected through thewireless channel.

The data transmitted from the transmitter 101 is received and processedby the coherent receiver 102A, 102B . . . 102N and non-coherent receiver103A, 103B . . . 103N simultaneously. The transmitter 101 transmits thedata over ternary alphabet {0,−1,+1}. The coherent receiver 102A, 102B .. . 102N demodulates the received signal over the ternary alphabet{0,−1,+1} while the non-coherent receiver demodulates the receivedsignal over the binary alphabet {0,1}.

The coherent receivers and the non-coherent receivers are representedinter-changeably by reference numerals 102 and 103 respectively orcoherent receivers 102A, 102B . . . 102N and non-coherent receivers103A, 103B . . . 103N for convenience throughout the specification.

FIG. 2 is a block diagram depicting data processing operation in anexemplary communication network, according to one embodiment of presentinvention.

In block 201 of FIG. 2, the data to be transmitted in digital form isrepresented. At the transmitter 101, the data is divided into a numberof data-blocks of length k referred to as data-symbols. Therefore, N=2^kdata symbols are encoded to N distinct ternary sequences. This encodingrequires number of distinct ternary sequences to be equal to N. Forexample, when the symbol size k=3, each of N=8 symbols are uniquelyencoded onto one of N=8 ternary sequences.

The transmitter draws the data-symbols from the symbol set s, whereS={s ₀ ,s ₁ , . . . ,s _(N-1) },N=2^(k).

These data-symbols are mapped onto one of the N possible ternarysequences from the code set C={c₀, . . . , c_(N-1)}. The mapping isrepresented as follows:s _(m) ∈S⇒c _(g) ∈C  (1)

Let us define interval set Z_(N)={0, 1, 2 . . . N−1}. Note that m,g∈Z_(N). The corresponding ternary sequences are transmittedsimultaneously to the non-coherent receiver 103A and coherent receiver102A.

When a ternary sequence is transmitted by the transmitter 101, thecoherent receiver 102A receives the ternary sequence as it is. Thenon-coherent receiver 103A receives the absolute of the ternary sequencetransmitted from the transmitter 101, i.e. the transmitted ternarysequence with the −1's received as +1's. Therefore, in order to transmitthe same ternary sequence to the coherent receiver 102A and non-coherentreceiver 103A effectively, the ternary sequences should belong to aternary code set C that satisfies the following properties.

a. The sequences in the ternary code set C should be maximally apart.

b. The sequences in the corresponding binary code set |C| consisting ofsequences obtained as the absolute of corresponding sequences in theternary code set C should be maximally apart.

The design of ternary code set C is achieved by designing a singlesequence with good autocorrelation properties over the binary alphabet{0,1} and the ternary alphabet {0,−1,+1}.

This sequence is referred as “base ternary sequence” hereafter in thecomplete specification.

The ternary code set C is obtained as the collection of all cyclicshifts of the said base ternary sequence. Let the base ternary sequencebe represented as t_(b), then the code set C is given byC={C _(g) :C _(g) =L ^(g) {t _(b) },∀g∈Z _(N)}  (2)

Here, L^(g){t_(b)} is the “cyclic shift by g” operator which cyclicallyshifts the base ternary sequence by “g” elements. It may be noted thatthe cyclic shift is applicable in any direction and whenever more thanone cyclic shift is considered, it is implied all cyclic shifts are inthe same direction.

The mapping in equation (1) can be rewritten ass_(m)⇒c_(g)=L^(g){t_(b)}.

We can now define a one to one mapping from the symbols set s to Z_(N)asg=ƒ(S _(m))  (3)

Here, ƒ(x) is any one to one mapping which maps the symbol s_(m)∈S tothe cyclic shift g∈Z_(N). For instance, g=ƒ(s_(m)) can be the decimalequivalent of binary symbol s_(m). Likewise, g=ƒ(s_(m)) can be thedecimal equivalent of the Gray mapping of symbol s_(m) or any other oneto one mapping that maps the data-symbol s_(m)∈S to the cyclic shift∈Z_(N). Therefore, each data-symbol is mapped to a unique cyclic shiftof the base ternary sequence.

The inverse mapping ƒ⁻¹(x) is defined asS _(m)=ƒ⁻¹(g)  (4)

In all the following discussions, we refer to the mapping in equation(3) as the one to one mapping and mapping described by equation (4) asthe inverse of one to one mapping.

FIG. 3 is a flow diagram illustrating a method of transmitting data,according to one embodiment of present invention. At step 301, a baseternary sequence is retrieved and stored in all the transmitters andreceivers. At step 302, one or more ternary sequences corresponding todata-symbols to be transmitted are obtained from the base ternarysequence. This step is explained in detail in FIG. 4. At step 303, theternary sequence is transmitted to the receiver.

At step 304 of FIG. 3, the receiver correlates the received signal withall cyclic shifts of the base ternary sequence, if the receiver is acoherent receiver 102A, 102B . . . 102N. Likewise, the non-coherentreceiver 103A, 103B . . . 103N demodulates the received signal bycorrelating the received signal with all cyclic shifts of the absoluteof the base ternary sequence.

At step 305, each of transmitted data-symbols is detected based on thecyclic shift corresponding to maximum correlation values among all the Ncorrelation values corresponding to all N cyclic shifts by mapping backsaid cyclic shift to the data-symbol using the inverse of one to onemapping.

In one embodiment, the transmission and reception can be explained asfollows. The transmitted signal corresponding to symbol s_(m)∈S(equivalently, c_(g)∈C) is represented as:c _(g)(t)=Σ_(n=0) ^(N-1) c _(g) [n]p(t−nT _(c))  (5)

Here, p(t) is the pulse shaping waveform and c_(g)[0], c_(g)[1], . . . ,c_(g)[N−1] refer to the elements of the ternary sequence c_(g). The chipduration is represented by T_(c). The transmitted signal correspondingto the ternary sequence c_(g)∈C (equivalently symbol s_(m)∈S) corruptedby Additive white Gaussian noise (AWGN) and other channel impairments isreceived at the receiver.

For instance, let y^(c) _(g)(t) and be y^(nc) _(g)(t) the basebandequivalent of the received signal at the coherent receiver 102 andnon-coherent receiver 103, respectively, corresponding to thetransmitted signal c_(g)(t). It may be noted that y^(nc) _(g)(t)=|y^(c)_(g)(t)|. For clarity, in the following discussions, the signal y^(c)_(g)(t) and y^(nc) _(g)(t) are referred as the “received ternarysequence” corresponding to the transmitted ternary sequence C_(g)∈C. Thereceived ternary sequence y^(c) _(g)(t) is demodulated by correlatingy^(c) _(g)(t) with all the cyclic shifts of the base ternary sequence,if the receiver is a coherent receiver. Likewise, the received ternarysequence y^(nc) _(g)(t) is demodulated by correlating y^(nc) _(g)(t)with all the cyclic shifts of absolute of the base ternary sequence.

This is described as follows.g∈Z _(N) asCorr_(g)=∫₀ ^(T) y ^(c) _(g)(t)c _(g)(t)dt, ∀g∈Z _(N)  (6)

Likewise, for non-coherent receiver, we haveCorr_(g)=∫₀ ^(T) y ^(nc) _(g)(t)|c _(g)(t)|dt, ∀g∈Z _(N)  (7)where,|C _(g)(t)|=Σ_(n=0) ^(N-1) |c _(g) [n]|p(t−nT _(c)).  (8)

The data-symbol is detected based on the single cyclic shiftcorresponding to maximum correlation values among all the N correlationvalues corresponding to N cyclic shifts. If we have the maximumcorrelation value as Corr_(max) corresponding to a cyclic shiftg=g_(estimate), then the data-symbol is detected ass _(m) ^(est)=ƒ⁻¹(g _(estimate))  (9)

FIG. 4 is flow chart illustrating a method of obtaining one or moreternary sequences corresponding to data-symbols to be transmitted fromthe base ternary sequence. At step 401, the transmitter divides the datato be transmitted into one or more data-symbols having a pre-definedlength. At step 402, each symbol from the set of data-symbols S ismapped onto one of the N possible ternary sequences from the code set Cobtained as cyclic shift of base ternary sequence. The process ofmapping and inverse mapping are explained in detail in equation 3 andequation 4.

FIG. 5 is a flow chart illustrating a method of generating a baseternary sequence, according to one embodiment of present invention. Atstep 501, a seed sequence of a pre-defined length is selected. The seedsequence can be an m-sequence or complement of an m-sequence. The lengthof seed sequence is N−1, where N=2^(n) is the desired length of the baseternary sequence. The weight of the sequence is N/2 if the seed sequenceis an m-sequence and the weight is (N−2)/2 if the seed sequence iscomplement of an m-sequence.

At step 502, it is determined whether the weight of selected seedsequence is a perfect square. In present invention, the weight of thesequence is the number of non-zero elements in a sequence. According toone embodiment of present invention, if the weight of the selected seedsequence is perfect square, then a perfect ternary sequence is generatedfrom the seed sequence as shown in step 503. The method of generating aperfect ternary sequence from a seed sequence is explained in detail inFIG. 6. If the weight of the selected seed sequence is not a perfectsquare, then a near perfect ternary sequence is generated from the seedsequence as shown in step 504. The method of generation of a nearperfect ternary sequence from a seed sequence according to step 504 isexplained in detail in FIG. 7.

At step 505, a pre-defined value is inserted in a pre-defined locationof the perfect ternary sequence or in the near perfect ternary sequencefor generating the base ternary sequence. The pre-defined value isdetermined based on the seed sequence selected for the perfect ternarysequence generation. The location for insertion of pre-defined value isthe location such that the MSAC of the resulting base ternary sequenceand absolute of the base ternary sequence is the least across allpossible locations. There exist two scenarios, one in which the value“1” is inserted in the perfect ternary sequence or in the near perfectternary sequence if the selected seed sequence used for the generationof perfect ternary sequence is an m-sequence. In another scenario, thepre-defined value inserted in the near perfect ternary sequence is thevalue “1” if the selected seed sequence is complement of an m-sequence.

FIG. 6 is a flow diagram illustrating the method of generating a perfectternary sequence from the seed sequence, according to one embodiment ofpresent invention. At step 601, one preferred pair of m-sequence isobtained using the seed sequence. The first m-sequence of the preferredpair is the seed sequence itself. The second m-sequence of the preferredpair is the m-sequence obtained as the pre-defined decimation of theseed sequence. The said pre-defined decimation that obtains anotherm-sequence from a given m-sequence is known art. In this context, apreferred pair of m-sequences of period P=N−1, where N=2″ is a pair ofm-sequence x and y with the crosscorrelation sequence θ(x,y) assumingthe values from the

${set}{\left\{ {{- 1},{{- 1} \pm 2^{\frac{n + 1}{2}}}} \right\}.}$The k^(th) element of the sequence θ(x,y) is given byθ(x,y)[k]=Σ _(i=0) ^(P-1)(−1)^((x) ¹ ^(⊕y) ^((i+k)mod P) ⁾,0≤k≤P−1  (10)

At step 602, the correlation sequence θ(x,y) of the preferred pair isobtained using equation (10).

At step 603, an offset correlation sequence ψ^((x,y)) from thecorresponding correlation sequence θ(x,y) is obtained. The offsetcorrelation sequence is obtained by adding the value “1” to each elementin the correlation sequence. That is, ψ^((x,y))=1+θ(x,y). The elementsof ψ^((x,y)) assume the values

$\psi^{({x,y})} \in \left\{ {0,{\pm 2^{\frac{n + 1}{2}}}} \right\}$

At step 604, the perfect ternary sequence is generated based on theoffset correlation sequence. In order to generate the perfect ternarysequence, offset correlation sequence ψ^((x,y))=1+θ(x,y) is divided by

$2^{\frac{n + 1}{2}}$resulting in a sequence Λ(x,y) with elements {0,±1}.

The method steps described in step 602, step 603 and step 604 isillustrated with the following example for obtaining a perfect ternarysequence of length 7.

This is demonstrated in the following example with the m-sequence ofperiod 7. Let the m-sequence x be selected as the seed sequence and them-sequence y together with m-sequence x form a preferred pair.

Let x={0 1 1 1 0 1 0}

AND, y={0 1 0 1 1 1 0}

Then, we have the cross correlation θ(x,y) given byθ(x,y)=(−1 −1 −5 3 3 −1 3)ψ=1+θ(x,y)=(0 0 −4 4 4 0 4)

And, consequently the sequence A(x,y) is obtained as

$\frac{1 + {\theta\left( {x,y} \right)}}{4} = \left\{ {{0\mspace{11mu} 0} - {1\mspace{11mu} 1\mspace{11mu} 1\mspace{11mu} 0\mspace{11mu} 1}} \right\}$

The sequence Λ(x,y) is a perfect ternary sequence with θ(x,y)={4000000}.Also note that the sequence Λ(x,y) is also a cyclic shift of theabsolute of the seed m-sequence x.

FIG. 7 is a flow diagram illustrating a method of generating a nearperfect ternary sequence, according to one embodiment of presentinvention. The near perfect ternary sequence is generated from the seedsequence if weight of the seed sequence is different from a perfectsquare. At step 701, one or more candidate sequences are obtained byinverting value of one or more positions corresponding to 1's in theseed sequence for a pre-defined ratio. In this context, invertingchanges the “1” to “−1”.

According to one embodiment of present invention, candidate sequencesare obtained by inverting all possible combinations of 1's in thesequence such that the ratio of number of −1's to +1's in the obtainedsequences are in the pre-defined ratio range. The said pre-defined ratiorange refers to all ratios between ⅓ and ⅔.

At step 702, at least one sequence out of the candidate sequences isselected based on the least value of mean squared autocorrelationcoefficient (MSAC) as the near perfect ternary sequence. The MSAC isbeing computed as the mean of N−1 out?of-phase squared autocorrelationcoefficients. Therefore, a near perfect ternary sequence is obtained bycarrying a computer search over these ratios. The sequence with leastvalue of mean squared autocorrelation (MSAC) is selected.

The mean squared autocorrelation of a sequence of length P is definedas:

$\begin{matrix}{\mu_{MSAC} = {\frac{1}{\left( {N - 1} \right)}{\sum\limits_{\tau = 1}^{P - 1}{R(\tau)}^{2}}}} & (11)\end{matrix}$

Here, P=N−1 is the length of the seed sequence and R(t) is the periodicautocorrelation of the sequence at delay τ, given byR(τ)=Σ_(i=0) ^(P-1) x _(i) y _(i+τ)  (12)

The base ternary sequences for length 8, 16 and 32 are shown in Tabletwhen the seed sequence is an m-sequence.

TABLE 1 Perfect ternary sequence/ Near perfect ternary Length BaseTernary sequence sequence 8 1 1 −1 0 0 1 0 0; 1 1 −1 0 0 1 0 0 1 1 −1 00 1 0; 1 0 1 1 −1 0 0 0; 0 1 0 1 1 −1 0 0; 0 0 1 0 1 1 −1 0 16 1 1 0 0−1 0 0 0 1 0 1 1 −1 1 1 −1 1 0 1 0 0; 0 1 0 1 1 0 1 1 −1 1 0 1 0 1 0 0−1 0 0 1 0 0 −1 0 0 0 0 1 1 1 1 0 −1 0 1 0 1 1 1 1 −1 0 0 1 0 0 0 0 −1 01 −1 0 0 1 0 0 32 1 1 −1 1 −1 0 0 0 1 −1 0 0 1 0 1 1 0 0 1 1 −1 1 0 1 −1−1 0 1 0 −1 1 −1 0 0 0 1 1 0 1 −1 0 0 0 0 −1 0 0 1 0 −1 0 1 0 −1 0 0 0 01 1 0 0 0

The base ternary sequences for length 8, 16 and 32 are shown in Table 2when the seed sequence is complement of an m-sequence. Please note thatmultiple base ternary sequences with similar MSAC are obtained and allare given in Table 1 and Table 2.

TABLE 2 Near perfect ternary Length Base Ternary sequence sequence 8 0 00 1 −1 0 1 1; 0 0 0 1 −1 0 1 1 0 0 0 1 −1 0 1 16 −1 0 0 0 0 1 0 −1 −1 00 0 0 1 0 0 0 1 1 0 1 1 −1 0 0 1 1 0 1 1; 1 1 −1 0 0 0 0 1 0 −1 0 0 1 10 1 1; 1 1 −1 0 0 0 0 1 0 −1 0 0 1 1 0 1 32 −1 0 0 1 0 1 −1 0 0 −1 −1 1−1 0 1 −1 −1 1 −1 0 1 0 1 0 1 0 0 0 1 0 0 0 0 1 0 0 1 1 0 1 1 −1 0 0 0−1 0 0 0 0 0 1 1 0 0 1 −1 0 0 1 0 1 −1

The sequences in Table 2 have less number of consecutive non-zeroelements, which may be desired in receiver design. From all thesequences listed in Table 2, sequences with uniform distribution of zeroand non-zero elements are selected to obtain the con-solidated list ofbase ternary sequences shown in Table 3.

TABLE 3 Perfect ternary sequence/ Near perfect ternary Length BaseTernary sequence sequence 8 0 0 0 1 −1 0 1 1 0 0 0 1 −1 0 1 16 1 −1 0 00 0 1 0 −1 0 0 0 0 1 0 −1 −1 0 0 1 1 0 1 1 0 0 1 1 0 1 1 32 −1 0 0 1 0 1−1 0 −1 −1 1 −1 0 1 0 0 −1 −1 1 −1 0 1 0 1 0 0 0 1 0 0 1 1 0 0 0 1 0 0 11 −1 0 0 0 0 0 1 1 −1 0 0 0 0 0 1 −1 0 0 1 0 1 −1 1

In an exemplary embodiment of present invention, the cyclic shifts ofthe base ternary sequences of length 8, 16 and 32 presented in the Table3. These are used for encoding the data-symbols of size k=3, k=4 andk=5, respectively before transmission. These base ternary sequences inTable 3 are referred as ⅜-OOK, 4/16-OOK and 5/32-OOK, respectively.Here, “OOK” stands for ON-OFF keying. Table 4 represents the baseternary sequences in Table 3 with the respective nomenclature.

TABLE 4 Basic Ternary spreading k length Nomenclature sequence 3 8⅜-OOK, 0 0 0 1 −1 0 1 1 4 16 4/16-OOK 1 −1 0 0 0 0 1 0 −1 0 0 1 1 0 1 15 32 5/32-OOK −1 0 0 1 0 1 −1 0 −1 −1 1 −1 0 1 0 1 0 0 0 1 0 0 1 1 −1 00 0 0 0 1 1

According to the embodiments of the present disclosure, the nomenclatureof the sequence ⅜-OOK, 4/16-OOK and 5-32-OOK as referred in Table 4, canbe also be provided with alternative nomenclature series such as ⅜Ternary OOK (⅜-TOOK), 4/16 Ternary OOK( 4/16-TOOK) and 5/32 Ternary OOK(5/32-TOOK) and ⅜ Ternary ASK(⅜-TASK), 4/16 Ternary ASK( 4/16-TASK) and5/32 Ternary ASK( 5/32-TASK) respectively. Here “ASK” refers toAmplitude shift keying.

Table 5 shows an example of mapping the data-symbols for k=3 onto cyclicshifts of the base ternary sequence of length 8, wherein eachcyclic-shift of the base ternary sequence is obtained as the decimalequivalent of the corresponding binary representation of thedata-symbols. As described earlier, any other one to one mappingdescribed by equation (3) as mentioned in FIG. 2 may be used to map thedata-symbols onto different cyclic shifts of the base ternary sequence.

TABLE 5 Data- Cyclic shift symbol (Decimal equivalent) Ternary sequences000 0 0 0 0 1 −1 0 1 1 001 1 1 0 0 0 1 −1 0 1 010 2 1 1 0 0 0 1 −1 0 0113 0 1 1 0 0 0 1 −1 100 4 −1 0 1 1 0 0 0 1 101 5 1 −1 0 1 1 0 0 0 110 6 01 −1 0 1 1 0 0 111 7 0 0 1 −1 0 1 1 0

The autocorrelation function of base ternary sequence at an arbitrarydelay k could be expressed as followsR(k)=xp+qx+R ^(a)(N−k+1)+R ^(a)(k)  (13)

In the above expression, if ‘x’ a binary value, equal to ‘0’, when thebase ternary sequence is obtained from a perfect ternary sequence.

Likewise ‘x’ is equal to ‘1’, when the base ternary sequence is obtainedfrom the near perfect ternary sequence.

The elements ‘p’ and ‘q’ represent those elements which align with theelement x′ at any delay k. The term R^(a)(k) is the aperiodicautocorrelation coefficient of the defined asR ^(a)(k)=Σ_(i=0) ^(N-k-1) c _(i) c _(i+k)  (14)

Here, c={c₀, c₁, c₂, . . . , c_(N-1)} is the sequence for which theaperiodic autocorrelation coefficient is being computed.

An example of generation of perfect ternary sequence {00-11101} isexplained below with an example.

Consider that ‘x’ is inserted before the third hit to result in sequenceas shown below. {00x-11101}

For arbitrary shift k=5, then the relative positioning of elements ofthe sequence and its shifted replica as:

$\begin{matrix}0 & 0 & x & {- 1} & 1 & 1 & 0 & 1 \\{- 1} & 1 & 1 & 0 & 1 & 0 & 0 & x\end{matrix}$

The autocorrelation at delay k=5, is given below:R(k)=x1+1x+R ^(a)(3)+R ^(a)  (5)

In the above computation, it happens that p=q=1.

When the base ternary sequence is obtained from a perfect ternarysequence, we have x=0. Therefore, R(k) is modified asR(k)=R ^(a)(N−k+1)+R ^(a)(k)  (15)

In order to limit the maximum value of (k) for ∀k∈[1,N−1] it issufficient to minimize the value of R^(a)(k)∀k∈[1,N−1] by selectingappropriate phase of the seed sequence. However, no known result forphase of the seed sequence is known in the literature to minimize theaperiodic autocorrelation across both the binary and the ternaryalphabets. However, if only a binary alphabet is considered theautocorrelation property of the sequence is determined by the aeriodicautocorrelation property of the binary sequences. This fact is used tocompute the autocorrelation of binary sequences obtained by extension ofknown sequences such as the extended m-sequences.

The insertion of x=0 at location corresponding to minimum value of MSACof the resulting base ternary sequence and the absolute of the baseternary sequence ensures that the equation (15) is least for differentvalues of the delay k.

FIG. 8 is block diagram of a transmitter, according to one embodiment ofpresent invention. According to one embodiment of present invention, thetransmitter includes a data input module 801, symbol generating module802, ternary sequence generating module 803, a base ternary sequenceretrieving module 804, cyclic shift generation module 805 andtransmitting module 806.

In one embodiment of present invention, the data to be transmitted isfed to the data input module 801. The data input module 801 isoperatively coupled with the symbol generating module 802. The data inbinary format is divided into pre-defined length in order to generatedata-symbols. The symbol generating module 802 performs the abovementioned operation.

According to one embodiment of present invention, the base ternarysequence is stored in the transmitter 101. The base ternary sequenceretrieving module 804 retrieves the base ternary sequence and feeds itinto the ternary sequence generating module 803. The ternary sequencegenerating module 803 is coupled with base ternary sequence retrievingmodule 804 and symbol generating module 802. The ternary sequencegenerating module 803 generates one or more ternary sequence from thebase ternary sequence by mapping each symbol onto corresponding ternarysequences obtained as cyclic shifts of the base ternary sequence basedon one to one mapping described in equation (3) in the description ofFIG. 2.

The transmitting module 806 according to one embodiment of presentinvention transmits the generated ternary sequences to the coherentreceiver 102A and non-coherent receiver 103A.

FIG. 9 is block diagram of a base ternary sequence generating module,according to one embodiment of present invention. The generation of baseternary sequence comprises selection of seed sequence, generation ofperfect ternary sequence, near perfect ternary sequence etc.

In one exemplary embodiment of present invention, the base ternarysequence generating module 900 comprises a seed sequence selectionmodule 901, a perfect ternary sequence generation module 902, a nearperfect ternary sequence generating module 903 and pre-defined valueinsertion module 904.

The seed sequence selection module 901 selects a seed sequence for thegeneration of base ternary sequence. The seed sequence can be anm-sequence or complement of an m-sequence. The selected seed sequence isof length N−1, where N is desired length of base ternary sequence to begenerated.

If the weight of the sequence is a perfect square, then the seedsequence is fed into perfect ternary sequence generation module 902. Ifthe weight of the seed sequence is not a perfect square, then theselected seed sequence is fed to the near perfect ternary sequencegeneration module 903.

The generation of perfect ternary sequence using the perfect ternarysequence generation module 902 comprises obtaining a preferred pair ofm-sequence using the seed sequence. Further, the perfect ternarysequence generating module 902 obtains the correlation sequence of thepreferred pair. The correlation sequence is obtained as the crosscorrelation function between the two sequences of the preferred pair.Then, an offset correlation sequence is obtained from the correspondingcorrelation sequence and the perfect ternary sequence is generated basedon the offset correlation sequence.

The generation of near perfect ternary sequence by a near perfectternary sequence generation module 903 includes, when weight of the seedsequence is different from a perfect square. The generation of nearperfect ternary sequence

comprises obtaining one or candidate sequences by inverting all possiblecombinations of 1's in the seed sequence such that the ratio of numberof −1's to +1's in the obtained sequences are in the pre-defined ratiorange and selecting at least one sequence out of the candidate sequencesbased on the least value of mean squared autocorrelation coefficient(MSAC) as the near perfect ternary sequence.

The pre-defined value insertion module 905 inserts a pre-defined valuein a pre-defined location of one of the perfect ternary sequence and thenear perfect ternary sequence for generating the base ternary sequence.The pre-defined location for insertion of pre-defined value is thelocation such that the MSAC of the resulting base ternary sequence andabsolute of the base ternary sequence is the least across all possiblelocations. The pre-defined value inserted is ‘0’, if the seed-sequenceis an m-sequence. The pre-defined value inserted is ‘1’ if theseed-sequence is complement of an m-sequence.

FIG. 10 is a block diagram of a receiver 102, according to oneembodiment of present invention. The receiver can be a coherent ornon-coherent type. The typical receiver comprises a signal receivingmodule 1001, a demodulating module 1002, a cyclic-shift-sequence inputmodule 1003 and a symbol detection module 1004.

The signal receiving module 1001 receives the signal transmitted fromthe transmitter 101. The received signal is demodulated using thedemodulation module 1002. The demodulation is performed by correlatingthe received signal with all the cyclic shifts of the base ternarysequence if the receiver is a coherent receiver. If the receiver is anon-coherent receiver, then demodulation is performed by correlating thereceived signal with all the cyclic shifts of the absolute of the baseternary sequence. The cyclic shifts of the base ternary sequence andabsolute of base ternary sequence is provided by a ternary sequenceinput module 1003. The values of the correlations are fed into a symboldetection module 1004. The symbol detection module 1004 identifies thedata-symbols from the cyclic shift corresponding to maximum value ofcorrelation by mapping back the cyclic shift to the data-symbol usingthe inverse of one to one mapping.

FIG. 11 is a block diagram of an exemplary communication device showingvarious components for implementing embodiments of the presentinvention. The communication device 1100 can be a transmitter or areceiver. In FIG. 11, the communication device 1100 includes a processor1101, a memory 1104, a read only memory (ROM) 1102, a transceiver 1106,and a bus 1103.

The processor 1102, as used herein, means any type of computationalcircuit, such as, but not limited to, a microprocessor, amicrocontroller, a complex instruction set computing microprocessor, areduced instruction set computing microprocessor, a very longinstruction word microprocessor, an explicitly parallel instructioncomputing microprocessor, a graphics processor, a digital signalprocessor, or any other type of processing circuit. The processor 1102may also include embedded controllers, such as generic or programmablelogic devices or arrays, application specific integrated circuits,single-chip computers, smart cards, and the like.

The memory 1104 and the ROM 1102 may be volatile memory and non-volatilememory. The memory 1104 includes a base ternary sequence generatingmodule 1105 generating a base ternary sequence according to one or moreembodiments described in FIG. 5. A variety of computer-readable storagemedia may be stored in and accessed from the memory elements. Memoryelements may include any suitable memory device(s) for storing data andmachine-readable instructions, such as read only memory, random accessmemory, erasable programmable read only memory, electrically erasableprogrammable read only memory, hard drive, removable media drive forhandling compact disks, digital video disks, diskettes, magnetic tapecartridges, memory cards, and the like.

Embodiments of the present subject matter may be implemented inconjunction with modules, including functions, procedures, datastructures, and application programs, for performing tasks, or definingabstract data types or low-level hardware contexts. The base ternarysequence generating module 1105 may be stored in the form ofmachine-readable instructions on any of the above-mentioned storagemedia and may be executable by the processor 1102. In one embodiment,the program may be included on a compact disk-read only memory (CD-ROM)and loaded from the CD-ROM to a hard drive in the non-volatile memory.The transceiver 1106 is capable of transmitting and receiving data. Thebus 1103 acts as interconnect between various components of thecommunication device 104.

The present embodiments have been described with reference to specificexample embodiments. It will be evident that various modifications andchanges may be made to these embodiments without departing from thebroader spirit and scope of the various embodiments. Furthermore, thevarious devices, modules, and the like described herein may be enabledand operated using hardware circuitry, firmware, and/or softwareembodied in a machine readable medium. Although the embodiments hereinare described with various specific embodiments, it will be obvious fora person skilled in the art to practice the invention withmodifications. However, all such modifications are deemed to be withinthe scope of the claims. It is also to be understood that the followingclaims are intended to cover all of the generic and specific features ofthe embodiments described herein and all the statements of the scope ofthe embodiments which as a matter of language might be said to fallthere between.

What is claimed:
 1. A method of data-symbol-to-chip mapping, the methodcomprising: generating data symbols based on input bits; and mapping thedata symbols to a set of ternary sequences, wherein the mapping isdetermined by a modulation format, and wherein the set of ternarysequences comprises a ternary sequence c₀ and a ternary sequence c_(m),the c_(m) being cyclic shifted from the c₀ by m locations, the m beingan integer.
 2. The method of claim 1, wherein the modulation format is aTASK (ternary amplitude shift keying).
 3. The method of claim 1, whereinthe c_(m) is a cyclic shifted from the c₀ by them locations to a right.4. The method of claim 3, wherein: the c₀ is {0 0 0 1 −1 0 1 1} in caseof the modulation format being 3/8-TASK (ternary amplitude shiftkeying), and the c₀ is {−1 0 0 1 0 1 −1 0 −1 −1 1−1 0 1 0 1 0 0 0 1 0 01 1 −1 0 0 0 0 0 1 1} in case of the modulation format being 5/32-TASK.5. The method of claim 1, wherein in case of the modulation format being3/8-TASK, a number of the data symbols are 8, and wherein the 8 datasymbols are mapped to 8-length ternary sequences.
 6. The method of claim1, wherein in case of the modulation format being 3/8-TASK, the c₀corresponding to a data symbol “0” is obtained, the c₀ being {0 0 0 1 −10 1 1}.
 7. The method of claim 1, wherein a length of the ternarysequences is 2^(k), the k being a size of the data symbols.
 8. Anapparatus for performing data-symbol-to-chip mapping, the apparatuscomprising: a processor configured to generate data symbols based oninput bits, and map the data symbols to a set of ternary sequences,wherein the mapping is determined by a modulation format, and whereinthe set of ternary sequences comprises a ternary sequence c₀ and aternary sequence c_(m), the c_(m) being cyclic shifted from the c₀ by mlocations, the m being an integer.
 9. The apparatus of claim 8, whereinthe modulation format is a TASK (ternary amplitude shift keying). 10.The apparatus of claim 8, wherein the c_(m) is cyclic shifted from thec₀ by the m locations.
 11. The apparatus of claim 10, wherein: the c₀ is{0 0 0 1 −1 0 1 1} in case of the modulation format being3/8-TASK(ternary amplitude shift keying), and the c₀ is {−1 0 0 1 0 1 −10 −1 −1 1 −1 0 1 0 1 0 0 0 1 0 0 1 1 −1 0 0 0 0 0 1 1} in case of themodulation format being 5/32-TASK.
 12. The apparatus of claim 8, whereinin case of the modulation format being 3/8-TASK, a number of the datasymbols are 8, and wherein the 8 data symbols are mapped to 8-lengthternary sequences.
 13. The apparatus of claim 8, wherein in case of themodulation format being 3/8-TASK, the c₀ corresponding to a data symbol“0” is obtained, the c₀ being {0 0 0 1 −1 0 1 1}.
 14. The apparatus ofclaim 8, wherein a length of the ternary sequences is 2^(k), the k beinga size of the data symbols.